Pith Number

pith:BJK64JE4

pith:2019:BJK64JE4HH4YSY3K3D2GLLEAD4

not attested not anchored not stored refs pending

Sharp systolic inequalities for $3$-manifolds with boundary

Eduardo Longa

arxiv:1912.08798 v4 · 2019-12-18 · math.DG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BJK64JE4HH4YSY3K3D2GLLEAD4}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-07-05T01:48:07.425246Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0a55ee249c39f989636ad8f465ac801f383760c052291be51e60ca27a1cb54a1

Aliases

arxiv: 1912.08798 · arxiv_version: 1912.08798v4 · doi: 10.48550/arxiv.1912.08798 · pith_short_12: BJK64JE4HH4Y · pith_short_16: BJK64JE4HH4YSY3K · pith_short_8: BJK64JE4

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BJK64JE4HH4YSY3K3D2GLLEAD4 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 0a55ee249c39f989636ad8f465ac801f383760c052291be51e60ca27a1cb54a1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ac4d51f606f1744d0d661cafbef21795666b63ab6d8b690c9c46ea46d0d82fd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2019-12-18T18:52:22Z",
    "title_canon_sha256": "2c85c4c34cecd8dbbb9ee55a49b535c8cea86424b0dedff3a506c0d6e5dfdbb3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1912.08798",
    "kind": "arxiv",
    "version": 4
  }
}